** **0.** Introduction**

The following three propositions form an inconsistent triad:

P) I do not know that I’m not in the matrix*

Q) I know that X

R) If I know that X, then I know that I am not in the matrix

(X is to be thought of as a proposition with content about the external world, such as ‘it is 3PM’ or ‘I am wearing trousers’, etc, rather than ‘I believe it is 3PM’ or ‘I am receiving sense-data about wearing trousers’, whose content is *internal* to the subject.)

We can represent the logical form of the propositions as follows, where p = ‘I know I am not in the matrix’, and q = ‘I know that X’:

P) ~p

Q) q

R) q → p

There are three ways that we can formulate an argument using these propositions which generate three positions about knowledge, which I am calling ‘skepticism’, ‘falliblism’ and ‘anti-skepticism’. Each argument is derived by having two of the propositions as premises with the negation of the remaining one as the conclusion.

**Skepticism**

The skeptic formulates her argument as follows:

R) If I know that X, then I know that I am not in the matrix

P) I do not know that I am not in the matrix

~Q) Therefore, I do not know that X

This argument has the form of modus tollens:

q → p

~p

Therefore ~q

2. **Fallibilism**

In contrast, the fallibilist argues from the truth of P and Q to the falsity of R, i.e.:

P) I do not know that I am not in the matrix

Q) I do know X

~R) Not-(if I know that X, then I know that I am not in the matrix)

This has the form:

~p

q

Therefore, ~(q → p)

What does this rearrangement say? It says that because we do know something, yet we do not know whether we are in the matrix, it follows that knowing that we are not in the matrix it is not a necessary condition for knowledge. Thus one can have knowledge without being able to rule out the skeptical hypothesis.

3. **Anti-Skepticism**

The final combination, the anti-fallibilist (which perhaps represents G.E. Moore?), runs as follows:R) If I know that X, then I know that I am not in the matrix

Q) I know that X

~P) I know that I’m not in the matrix

The form of this argument is modus ponens:

q → p

q

Therefore, p

On this argument, the requirement of ruling out the matrix as a necessary condition for knowledge is accepted, and the fact of knowledge of X is affirmed, with the consequence that one knows they are not in the matrix. A refutation of the skeptical hypothesis has been achieved (hence the name ‘anti-skepticism’).

4. **How to choose? **

So now we have three rival arguments, each of which picks two of the members of the triad and rejects the third. The question of which argument to pick turns then, not on logic as such, but on the question of which proposition to jettison. Which one seems the least plausible? The problem is that they all seem eminently plausible.

P says that you cannot rule out the matrix, or evil daemon hypothesis. It seems very plausible, at least to anyone who has read Descartes or watched the Matrix. Denying this premise seems to require a refutation of skepticism.

Q says that you know that X. This is obviously going to depend on your choice of X, but why not make X as plausible as you like? Let X be ‘it is now 3PM’ (if it is 3PM), or that you are wearing trousers (if you are wearing trousers), etc. It can be the most run of the mill, ordinary knowledge claim you can think of. By definition, Q should be very plausible, if any knowledge claim at all can be. And P, Q and R are all knowledge claims.

R says that if you know that you are walking down the street, or that it is 3PM, or that you are wearing trousers, or whatever, then you know you are not in the matrix. This is also very difficult to deny. If I know that I am walking down the street, then it is true that I am walking down the street. If it is true that I am walking down the street, then I am not in the matrix. Thus, if I know I am walking down the street then I am not in the matrix. Therefore, it seems that if I know that X, then I know I am not in the matrix.

Where is the weak link here?

*for ‘in the matrix’, feel free to substitute in ‘am a brain in a vat’, ‘am being deceived by a Cartesian daemon’, etc.